Nearly half the 20 applicants given initial approval for medical marijuana dispensaries have been eliminated after a second review, state health officials announced Friday — including both in Boston and all three run by former Massachusetts congressman William Delahunt.

Reasons for rejection ranged from questionable corporate structures that appeared to divert revenues from the non-profit dispensaries to for-profit affiliates; misrepresenting local support; and omitting one investor’s drug conviction.

Only 11 dispensaries will be given provisional certificates allowing them to set up operations and undergo inspections, Karen van Unen, executive director of the state’s medical marijuana program, said during a news conference.

She said some dispensaries could open by November, but most wouldn’t until February; state officials originally envisioned most would open this summer. She said 97 percent of the state’s population will live within 30 miles of a dispensary.

The contentious, high-stakes selection process was delayed for months after the media and losing applicants raised concerns about misrepresentations, financial arrangements, and conflicts of interest involving several of the companies approved in January for provisional dispensary licenses, as well as the backgrounds of some of their principals.

These companies can reapply next year, when a new round of applications will likely be considered, van Unen said.

In a letter to Delahunt’s company, van Unen said it was denied licenses because it planned to divert excessive gross revenues to a management company, and made “incorrect representations” on its application that suggested it had support from state Senate President Therese Murray.

A marijuana dispensary “must operate on a non-profit basis for the benefit of registered qualifying patients,” Van Unen wrote. Delahunt’s company, she said, “could not substantiate the reasonableness of the fee’’ it planned to pay to the management company, which amounted to an estimated $10.6 million over the first three years.

When pressed about how it had arrived at that amount, Medical Marijuana of Massachusetts admitted it was “arbitrary,” van Unen wrote.

Delahunt’s company said on its application that in an effort to obtain assurances of support or non-opposition for its Plymouth dispensary, it met with more than a dozen officials, including Murray.

Van Unen said in her letter that Delahunt, the chief executive of Medical Marijuana, admitted during an interview with state officials that his meeting with Murray “was simply informative and no request was made for her support.”

Delahunt issued a statement, saying, “We worked very hard to get this right at every turn, legally and ethically, so we’re obviously surprised and disappointed. But frankly, I’m also perplexed, because the corporate structure cited as the main reason for our denial is the same one that was in place when we were rated #1 among applicants in the last round and received the Department’s green light to proceed.”

He added that his team would review the decision, “with the intention of providing clarifications of any findings that warrant them and to weigh our options going forward.”

State officials have acknowledged they hadn’t checked the veracity of applicants’ claims before the January announcement, despite spending more than $600,000 on two contractors who were hired to scour the backgrounds and evaluate their proposals. Regulators said they have since dug extensively into company executives’ backgrounds, finances, and business plans.

At Friday’s news conference, van Unen said the fact that the latest review found so many problems should not shake the public’s confidence in the process.

“I say it’s fabulous,” she said. “I am delighted to be at this point.”

The selection process has been shrouded in secrecy, with state health officials refusing to release the documents showing in detail how they evaluated and scored each of the 100 applicants that vied for the first batch of licenses awarded by the state. Those documents were finally released Friday afternoon.

Several lawsuits have been filed, and state lawmakers launched an investigation into the fairness of the licensing process, which was authorized by voters in a 2012 referendum. Massachusetts is one of 22 states that has legalized medical use of marijuana.

Another of the companies knocked out by regulators Friday, Good Chemistry of Massachusetts, had proposed locations in Boston and Worcester. In a letter to the company, van Unen cited claims in its license applications that it had support from local officials, which the officials contested.

Green Heart Holistic, a California-based company that had planned to open in Boston’s South End, was told it was deemed unsuitable because its application didn’t mention that the chief executive’s brother and business partner had once been convicted of a marijuana-related felony.

Debilitating Medical Condition Treatment Centers was denied a dispensary license for Holyoke because its president, Heriberto Flores, earned a combined salary of $900,000 from two nonprofits and was expected to make at least $300,000 for managing the dispensary, state officials said.

In a rejection letter to the company, van Unen wrote that a state audit last month revealed that Flores was paid $450,000 for working full time on behalf of the New England Farm Workers Council, which provides services to the Massachusetts Department of Transitional Assistance.

At the same time, Flores was collecting $450,000 as the chief executive and full-time employee of another, affiliated nonprofit.

A lawyer for Flores and Debilitating Medical Condition Treatment Centers issued a statement calling the state’s action unfair and improper, saying it was based on “a gross misunderstanding” of the audit, which is being challenged by the New England Farm Workers Council.

The attorney, William M. Bennett of Springfield, said he was confident Flores would be vindicated.

As with Delahunt’s company, state officials objected to the financial structure of Brighton Health Advocates. A letter from van Unen said that Brighton’s application for a Fairhaven dispensary indicated that a for-profit management company, comprising Brighton’s top executives, would be paid “20% of the non-profit’s gross revenues; a 30% upcharge on employee salaries; lease payments under a sublease that doubled the rent charge; and repayments under a promissory note that almost doubled the interest rate.”

Ernie Corrigan, a company spokesman, said, “We changed the management structure in response to questions raised during the review process, and we are frankly at a loss to understand how we didn’t respond specifically to the concerns they raised.”

Greeneway Wellness Foundation, which won provisional approval for a dispensary in Cambridge and had applied for two additional sites, was rejected for questionable finances. Applicants were required to show evidence of at least $500,000 in capital for a single application, and $400,000 for each subsequent application.

Greeneway’s application showed three savings accounts with a total of $1.3 million, state regulators said, but on the day after the applications were submitted to the state, Greeneway pulled all of its money out and returned it to its “alleged investors,” said a letter from van Unen.

When questioned about its finances, Greeneway showed regulators bank statements and letters from 30 different “investors” that said they were “custodians” holding the funds for Greeneway, but the letters were created in early June, months after the $1.3 million was returned to the original investors, van Unen’s letter noted.

John Greene, chief executive of the company, did not return a phone call seeking comment.

Anthony Richard, who is listed as the company’s chief financial officer in its application, said in an interview that he was unaware of the company’s finances, had been introduced to Greene last fall through a mutual friend, and only agreed to be involved with the company if it won a license.